Second Order Differential Equations with Transcendental Coefficients
Copyright policy )Second Order Differential Equations with Transcendental Coefficients
Let w 1 {w_1} and w 2 {w_2} be two linearly independent solutions to w + A w = 0 w + Aw = 0 , where A A is a transcendental entire function of order ρ ( A ) > 1 \rho (A) > 1 . We show that the exponent of convergence λ ( E ) \lambda (E) of the zeros of E = w 1 w 2 E = {w_1}{w_2} is either infinite or satisfies ρ ( A ) − 1 + λ ( E ) − 1 ≤ 2 \rho {(A)^{ - 1}} + \lambda {(E)^{ - 1}} \leq 2 . For ρ ( A ) = 1 2 \rho (A) = \tfrac {1}{2} , this answers a question of Bank.
Beurling-Tsuji estimate for harmonic measure, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, Ordinary differential equations in the complex domain
Beurling-Tsuji estimate for harmonic measure, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, Ordinary differential equations in the complex domain
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